Davis and Tozer, in either the 2nd or 3rd edition, added "The Chantey-man's Song." It seems clear to me that they modeled it off of the one-verse excerpt in LA Smith's (1888) collection. (Smith, in turn, was just reproducing Alden's 1882 article.) As in almost all the chanties they presented, however, Davis/Tozer made up lyrics. I believe they made up the verse,

I'm Chantyman of the working party
So sing, lads, pull, lads, so strong and hearty.

Perhaps "wild goose nation" would not scan for them. They continue on with some fanciful lyrics about wild geese.

Hugill seems to have liked the above lyric, and added it to his mix. Unless I'm mistaken, it does not appear elsewhere.

Davis/Tozer were evidently not acquainted with the song, otherwise they would not have based it verbatim on Smith. So we can assume they made up the lyric. And since Smith and Alden did not give it a title, D/T called it "The Chanty-man's Song."